Sum of the areas of two squares is `468\ m^2`. If the difference of their perimeters is 24 m, find the sides of the two squares.

Explanation

To solve the problem step by step, we will denote the sides of the two squares as \( x \) and \( y \).

### Step 1: Set up the equations based on the given information.
1. The area of the first square is \( x^2 \) and the area of the second square is \( y^2 \).
2. According to the problem, the sum of the areas of the two squares is given as:
\[ x^2 + y^2 = 468 \quad \text{(Equation 1)} \]
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